MECHANICS 65 



to an overhead support and the hoisting force is applied at the 

 other end in an upward direction. With this arrangement, a 

 pull of 1 Ib. at F will lift a weight of 2 Ib. at W. If the free 

 end of the rope is. carried up over a fixed pulley, as shown in 

 Fig. 3, the effect will still be the same; that is, a weight of 

 2 Ib. can be raised by a force F of 1 Ib.; that is, in Figs. 2 

 and 3, F=W. 



A double movable pulley is shown in Fig. 4; that is, the 

 movable block attached to the load W carries two pulleys. 

 A similar pulley is fixed to an overhead support, and one end 

 of the rope is attached to it, the other end being carried around 

 the several pulleys as shown. With this arrangement, a force 

 F of 1 Ib. is sufficient to raise a weight W of 4 Ib.; that is, 

 F = \W. 



Combination of Pulleys. By increasing the number of fixed 

 and movable pulleys over which the hoisting rope or chain 

 passes, the force required to lift a given load may be lessened. 

 In Fig. 5 is shown a quadruple movable pulley, or one hi which 

 the movable block has four pulleys, and a force of 1 Ib. at F 

 will lift a weight of 8 Ib. at W. The following general rule 

 applies to any combination of pulleys: 



Rule. When a single rope is used with a combination of 

 pulleys, a pull on the free end will balance a load on the movable 

 block as many times as great as the pull as there are parts of the 

 rope supporting the movable block 



For instance, in Figs. 2 and 3, there are two parts of the 

 rope supporting the movable block, and the load balanced by 

 the pull F is twice as great as the pull F. In Fig. 4 there are 

 four parts of the rope supporting the movable block, so that 

 W=F, or F = %W. In Fig. 5, W=8F, as there are eight 

 parts of the rope supporting the movable block. 



Differential Pulley. The arrangement shown in Fig. 6 is 

 known as a differential pulley. The two fixed pulleys have 

 different radii r and R. The hoisting chain passes around the 

 larger of the fixed pulleys, then around the movable pulley 

 carrying the weight W, and then around the smaller fixed 

 pulley. The chain is joined at its ends, thus forming a con- 

 tinuous piece. The two fixed pulleys are fastened together 

 so that they must turn as one piece on their axle. When a 



